Abstract
Computation by quantum parallelism involves associating a quantum state
v(f)
to each function
f
:
Z
m
→
Z
n
.
v(f)
is formed from superpositions of states labelled by the values of
f
, the standard choice being an equally weighted superposition of all the values of
f
. A joint property
G(f)
of the values
f
(0),...,
f
(
m
–1) is called computable by quantum parallelism (QPC) if there is an observable
g
which will reveal the value
G(f)
, with non-zero probability, when applied to
v(f)
, and will never show a false value. It is shown that the problem of deciding which
G
s are QPC can be formulated entirely in terms of the linear relations which exist among the
v(f)
s. In the case of
f
:
Z
m
→
Z
2
,
G
:(
Z
2
)
m
→
Z
2
we explicitly describe all properties which are QPC and show that this includes only
m
2
+
m
+ 2 of the 2
2
m
such properties. By using a suitable nonstandard definition for
v(f)
this number can be increased to 2
2
m
— 2
m+1
(for
m
> 1).
Reference2 articles.
1. Quantum theory, the Church–Turing principle and the universal quantum computer
2. Deutsch D. 1986 In Quantum concepts in space and time (ed. R. Penrose & C. Isham) pp. 215-225. Oxford: Clarendon Press.
Cited by
36 articles.
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